SOLUTION: If the height of an equilateral triangle is also a root of equation y^4-3y^2-270 then the area of the triangle in cm^2 is

Question 1064751: If the height of an equilateral triangle is also a root of equation y^4-3y^2-270 then the area of the triangle in cm^2 is
Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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There is NO equation in your post.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
y^4-3y^2-270=0
(y^2-18)(y^2+15)=0
y^2=18; y^2=-15, can exclude.
y=3 sqrt (2), only positive root
equilateral triangle has sides s
height is (s/2)sqrt(3)=3 sqrt (2)
Therefore, side is 6sqrt(2)/sqrt(3)
That is 6 sqrt(6)/3 by rationalizing, or 2 sqrt(6)
The area is 1/2 bh=1/2 *2 sqrt(6)*3 sqrt (2)=3 sqrt (12)=6*sqrt (3)
The area of an equilateral triangle with side s is s^2/4*(sqrt3)
Here, s^2=(2 sqrt(6))^2=4*6=24
Area is 24/4* (sqrt 3)=6 sqrt (3)

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